The article presents a new method of the structural analysis of the mechanisms using graphs, which allows us to determine the number of the excess and metric relationships, extra mobility and extra links, occurring in the circuits of the mechanisms. It shows implementation of this method in the form of a computer program for an automated structural analysis by computer mechanisms. The program was developed in the integrated environment of Microsoft Visual Studio, 2015. The program language was Visual C#. The graphical interface was built using the library component Net Framework 4. The authors'program for searching of the contours' mechanism applied to the graph algorithm is based on the search of "the depth". According to the formulas proposed by the authors, for each contour the program finds the number of the redundant ties, extra mobility, extra links, and metric connections. The calculation results of the program present the number of the circuits of the mechanism, their composition, the number of the redundant links or redundant mobility of the contours, the number of extra units and metric relations, as well as the number of the degrees of freedom of the mechanism and its mobility. The article presents an analysis of the mechanism of the mechatronic device with the developed program. Application of this method of analysis of the mechanisms ensures a rational construction of the mechanisms leading to reduction of friction and wear in the kinematics pairs, and improvement of the conditions of their functioning and the quality of operation of the mechanisms.